A scatterplot puts one point per individual, using two measurements as its coordinates.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
What to describe
Report direction, form and strength: whether it rises or falls, whether it is straight or curved, and how tightly the points follow it.
The correlation coefficient
r runs from −1 to 1. Its sign gives the direction and its size gives the strength of a straight-line relationship.
It measures straightness only
A perfect U-shaped relationship can have r near zero. A small r means no linear pattern, not no pattern.
Correlation is not causation
Ice cream sales and drownings rise together because both follow hot weather. Neither causes the other.
Lurking variables
The hidden third factor, here the weather, is a lurking variable. Only a controlled experiment can establish cause.
Direction, form and strength
A complete description of a scatterplot names all three, plus any unusual points. Positive or negative direction, linear or curved form, and how tightly the points cluster around the pattern.
What r measures
The correlation coefficient runs from −1 to 1 and measures the strength and direction of a linear relationship only. A perfect parabola has correlation near zero, which is not a failure of the data.
Correlation has real limitations
It only detects linear patterns, it is not resistant to outliers, and it has no units so it cannot be interpreted as a rate. A high r says the points are close to a line, nothing more.
Association is not causation
Ice cream sales and drownings correlate because both rise with temperature. A lurking variable explains the association with no causal link between the two. This is the single most misused statistic in public argument.
Step 2: Try It Yourself
Tap and try it out.
The slope is 1: for every 1 across, the line goes 1 up.
Step 3: Watch an Example
One step at a time.
Watch Kofi Describe a Scatterplot
Kofi has study hours against test scores for 20 students, with r = 0.82.
- Step 1
The points rise from left to right, so the direction is positive.
Step 4: Your Turn
Practice makes it stick.
The Sign
Problem 1 of 2
As one variable rises the other falls. Is r positive or negative? 1 positive, 2 negative.
The Ice Cream
Problem 2 of 2
Ice cream sales and drownings both rise in summer. Does one cause the other? 1 for yes, 0 for no.
Two at a Time
1 of 8
What is the largest value r can take?
2 of 8
What is the smallest value r can take?
3 of 8
r = 0.05. Strong or weak linear relationship? 1 strong, 2 weak.
4 of 8
r = −0.95. Strong or weak? 1 strong, 2 weak.
5 of 8
A perfect U-shaped relationship can have r near zero. True? 1 yes, 0 no.
6 of 8
What kind of study can establish causation? 1 observational, 2 controlled experiment.
7 of 8
Which must be reported when describing a scatterplot?
8 of 8
r = 0.9 between shoe size and reading level in children. Does shoe size cause reading? 1 yes, 0 no.
Step 5: Quick Check
Show what you know.
Question 1 of 2
r = −0.88. Is the relationship strong or weak? 1 strong, 2 weak.
Question 2 of 2
What is a lurking variable?
What You Learned
- Describe a scatterplot by direction, form and strength.
- r runs from −1 to 1 and measures only straight-line association.
- Correlation never establishes causation on its own.